4 ms·

Solomonoff induction is for just making predictions/models, AIXI is for when it needs to also take actions. Both AIXI and solomonoff induction can be approxima

by drdeca 8y ago

Solomonoff induction is for just making predictions/models, AIXI is for when it needs to also take actions. Both AIXI and solomonoff induction can be approximated arbitrarily closely, given sufficient computational resources. Human intelligence is generally expected to be computable because physics is generally believed to be computable. However, don't get me wrong: I would be quite excited and probably pleased to learn that it isn't. I just am not convinced enough (or really, convinced much at all) to hang anything important on the idea that it isn't computable.

yters 8y ago
Even given infinite resources Solomonoff induction cannot be computed, because we computationally cannot eliminate all non halting programs. Why believe human intelligence is limited by physics?
- xelxebar 8y ago
  Because elan vital and phlogiston turned out to be terrible ideas? Human cognition affects human action which has physical effects. So at the least, intelligence is causally linked with known phycial processes. I'd say that's sufficient to make it amenable to physical inquiry. Pulling out drastic measures like extraphysical magic, just to hand wave at an imprecise problem seems like an act of epistemic violence or something.
  - yters 8y ago
    Certainly intelligence is causally linked with the physical world, hence our conversation. But, this does not imply intelligence is itself physical. Additionally, saying intelligence is non physical does not turn it into some kind of inscrutable magic. Could you explain why you think this is the case? For example, I wrote an article explaining how modeling the human mind as a halting oracle results in empirically meaningful results. https://am-nat.org/site/halting-oracles-as-intelligent-agents/ https://am-nat.org/site/halting-oracles-as-intelligent-agent...
    - xelxebar 8y ago
      I think it depends on how we delineate physical vs non-physical. In this case, I'm taking a simple definition of "physical" to mean "anything amenable to scientific inquiry" or "any phenomenon that is, in principle, part of consensus reality". Actually, I'm confused what we'd even be claiming by calling intelligence purely non-physical. Perhaps you're thinking of the qualia of intelligence? Regarding the article you wrote, I think the concept of "partial oracle", while coherent, isn't super helpful. Or rather, it's too broad of a characterization. The halting problem doesn't claim that Turing machines can't solve some halting problems, it's that there's no finite class of turing machines which can together solve any halting problem. It's not precisely news that some Turing machines can solve the halting problem for certain (infinite) classes of machines. Case in point, regular languages. Anyway, meta-discussion-wise, I'm super happy to find kindred souls that also enjoy thinking about these things. I recently came across the Complexity Zoo[0] website, and if you're anything like me, I suspect you'll enjoy it too! [0]:https://complexityzoo.uwaterloo.ca/Complexity_Zoo https://complexityzoo.uwaterloo.ca/Complexity_Zoo
      - yters 8y ago
        I would disagree with that definition of physical. I believe a better definition of physical is anything that can be reduced to the laws of physics. Since the laws of physics are computable, I would enlarge the definition to be anything that can be reduced to a Turing machine. It's logically possible there are irreducible entities, i.e. partial oracles, so it is logically possible there are non physical, yet physically testable entities. In the article the point is a bit subtle, but partial oracles are still not Turing reducible. The point of the article is that the fact humans cannot solve all problems does not imply they are Turing reducible. At any rate, from my cursory analysis, it appears the notion of a non Turing reducible human mind is empirically tractable, so I still don't understand why it is not a viable scientific hypothesis and why AGI is assumed to be necessarily true. The mind as a partial oracle would imply AGI is impossible. Thanks for the link, I'll be checking it out!
        feanaro 8y ago
- drdeca 8y ago
  Solomonoff induction can be computed in the limit. During round i, simulate your chosen UTM on each valid input string (note: assuming that the valid input strings are prefix free, which iirc is the standard for solomonoff induction) of length at most i, until you have simulated it for i steps total, or until it halts (whichever comes first). When doing so, for any string, the proportion of the inputs (with respect to the coin flip measure thing) to the UTM that eventually halt with whatever particular output, which will have been found to halt , will approach "all of them". Now, you can't quite say "run as long as you need to in order to get answer within this epsilon of correct answer", because you don't have a way of determining whether something hasn't halted yet but will, or if it never will, but, it is still computable in the limit. If you use absurdly (possibly quite absurdly) large but finite amounts of computational resources, it should give you a good enough approximation. Humans make mental errors often enough. I don't see why one would think that, because solomonoff induction is only approximable, that that suggests human intelligence is uncomputable. Why not suppose that humans just have a very close approximation to the uncomputable thing, rather than the noncomputable thing itself? Why believe that human intelligence is computable? Well, for me it is more of a "choosing not to believe that it is uncomputable". If I believed it uncomputable, I might hang too much of my philosophy/worldview on that assumption, and then if I turned out to be incorrect on that, too much might come crashing down. Edit: note: I mean "not believing", not "disbelieving". Not(believe(p)) rather than believe(not(p)) .
  - yters 8y ago
    Ah, right. That's true. Since the elegant program is guaranteed to halt, then we'll get to it eventually. My mistake. That being said, even with infinite resources we will never know when that actually happens, so we still will never known when Solomonoff induction has succeeded. I don't see what will come "crashing down." Science is about being able to quantify and empirically test our hypotheses. Nothing about uncomputable intelligence seems to undermine this idea, but perhaps I am missing something. Instead, it broadens the range of hypotheses we can use to explain the world, which seems to be a good thing.
    - drdeca 8y ago

by drdeca 8y ago

yters 8y ago

Even given infinite resources Solomonoff induction cannot be computed, because we computationally cannot eliminate all non halting programs. Why believe human intelligence is limited by physics?

xelxebar 8y ago
Because elan vital and phlogiston turned out to be terrible ideas? Human cognition affects human action which has physical effects. So at the least, intelligence is causally linked with known phycial processes. I'd say that's sufficient to make it amenable to physical inquiry. Pulling out drastic measures like extraphysical magic, just to hand wave at an imprecise problem seems like an act of epistemic violence or something.
- yters 8y ago
  Certainly intelligence is causally linked with the physical world, hence our conversation. But, this does not imply intelligence is itself physical. Additionally, saying intelligence is non physical does not turn it into some kind of inscrutable magic. Could you explain why you think this is the case? For example, I wrote an article explaining how modeling the human mind as a halting oracle results in empirically meaningful results. https://am-nat.org/site/halting-oracles-as-intelligent-agents/ https://am-nat.org/site/halting-oracles-as-intelligent-agent...
  - xelxebar 8y ago
    I think it depends on how we delineate physical vs non-physical. In this case, I'm taking a simple definition of "physical" to mean "anything amenable to scientific inquiry" or "any phenomenon that is, in principle, part of consensus reality". Actually, I'm confused what we'd even be claiming by calling intelligence purely non-physical. Perhaps you're thinking of the qualia of intelligence? Regarding the article you wrote, I think the concept of "partial oracle", while coherent, isn't super helpful. Or rather, it's too broad of a characterization. The halting problem doesn't claim that Turing machines can't solve some halting problems, it's that there's no finite class of turing machines which can together solve any halting problem. It's not precisely news that some Turing machines can solve the halting problem for certain (infinite) classes of machines. Case in point, regular languages. Anyway, meta-discussion-wise, I'm super happy to find kindred souls that also enjoy thinking about these things. I recently came across the Complexity Zoo[0] website, and if you're anything like me, I suspect you'll enjoy it too! [0]:https://complexityzoo.uwaterloo.ca/Complexity_Zoo https://complexityzoo.uwaterloo.ca/Complexity_Zoo
    - yters 8y ago
      I would disagree with that definition of physical. I believe a better definition of physical is anything that can be reduced to the laws of physics. Since the laws of physics are computable, I would enlarge the definition to be anything that can be reduced to a Turing machine. It's logically possible there are irreducible entities, i.e. partial oracles, so it is logically possible there are non physical, yet physically testable entities. In the article the point is a bit subtle, but partial oracles are still not Turing reducible. The point of the article is that the fact humans cannot solve all problems does not imply they are Turing reducible. At any rate, from my cursory analysis, it appears the notion of a non Turing reducible human mind is empirically tractable, so I still don't understand why it is not a viable scientific hypothesis and why AGI is assumed to be necessarily true. The mind as a partial oracle would imply AGI is impossible. Thanks for the link, I'll be checking it out!
      - feanaro 8y ago
drdeca 8y ago
Solomonoff induction can be computed in the limit. During round i, simulate your chosen UTM on each valid input string (note: assuming that the valid input strings are prefix free, which iirc is the standard for solomonoff induction) of length at most i, until you have simulated it for i steps total, or until it halts (whichever comes first). When doing so, for any string, the proportion of the inputs (with respect to the coin flip measure thing) to the UTM that eventually halt with whatever particular output, which will have been found to halt , will approach "all of them". Now, you can't quite say "run as long as you need to in order to get answer within this epsilon of correct answer", because you don't have a way of determining whether something hasn't halted yet but will, or if it never will, but, it is still computable in the limit. If you use absurdly (possibly quite absurdly) large but finite amounts of computational resources, it should give you a good enough approximation. Humans make mental errors often enough. I don't see why one would think that, because solomonoff induction is only approximable, that that suggests human intelligence is uncomputable. Why not suppose that humans just have a very close approximation to the uncomputable thing, rather than the noncomputable thing itself? Why believe that human intelligence is computable? Well, for me it is more of a "choosing not to believe that it is uncomputable". If I believed it uncomputable, I might hang too much of my philosophy/worldview on that assumption, and then if I turned out to be incorrect on that, too much might come crashing down. Edit: note: I mean "not believing", not "disbelieving". Not(believe(p)) rather than believe(not(p)) .
- yters 8y ago
  Ah, right. That's true. Since the elegant program is guaranteed to halt, then we'll get to it eventually. My mistake. That being said, even with infinite resources we will never know when that actually happens, so we still will never known when Solomonoff induction has succeeded. I don't see what will come "crashing down." Science is about being able to quantify and empirically test our hypotheses. Nothing about uncomputable intelligence seems to undermine this idea, but perhaps I am missing something. Instead, it broadens the range of hypotheses we can use to explain the world, which seems to be a good thing.
  - drdeca 8y ago